Relativistic kinetic equations with mesonic degrees of freedom

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Abstract
We extend the same techniques found to be successful in condensed matter physics for deriving Boltzmann transport equations to the relativistic domain to facilitate the study of nonequilibrium phenomena where relativistic effects are important. Although the ensuing equations are discussed in the context of the relativistic heavy-ion system, the discussion is sufficiently general to cover other important physical situations such as those of astrophysical origin. Starting from an arbitrary local quantum field theory, we show how one may construct a Boltzmann transport equation and what the necessary assumptions that go into its construction are. To illustrate these techniques we derive a set of coupled Boltzmann equations with medium-dependent collision terms for relativistic fermions and spin-zero bosons interacting via a Yukawa coupling. We find that the dynamics may be described in terms of the fermion distribution function alone only under the very restrictive condition that the boson fields remain in local equilibrium throughout the collision process. Moreover, we find that one must go beyond the mass-shell constraint to find a physically reasonable boson production mechanism.